The ability is normally applied to allow him to manipulate vectors, though it has been shown that it is more than that, through the use of Accelerator's massive intellect and calculating prowess, thereby influencing his ability to understand unknown or strange laws that are unknown to him, and also making use of that particular law.[1]

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"One-way road" is the translation used for the kanji for Accelerator, and is most likely a reference to the act of him "redirecting" any vector coming towards him back.

The name is likely a reference to particle accelerators, though not in how particle accelerators work, like other particle accelerator-like abilities such as Synchrotron, but what the purpose of the particle accelerator is, which is to allow a researcher or scientist to get as close as possible to the truth that makes up the universe and the laws that govern it.[Excerpts 3] Accelerator could also come from the vector quantity of acceleration, which refers to a body's change of velocity over time, where Accelerator has shown that he can "accelerate" a body at rest, for example, the still pebble that Accelerator kicked towards Kamijou Touma being accelerated towards a dangerous speed.

Accelerator's ability is based on Vector Transformation (ベクトル変換,Bekutoru Henkan?),[Notes 1] known in other names such as Vector Change and Vector Conversion, that allows him to control vectors (magnitude and direction) and influence objects that have vectors such as bullets, heat, and electricity.[2] Accelerator is both passive and active in usage, or can even be referred to as defensive and offensive.[3][4]

It is self-evident that the ability requires a great amount of calculating power from the esper, as it requires for Accelerator to take into account several vectors that he wants to redirect, and when activated, several variables are present when manipulating and controlling vectors. For example, Accelerator is able to delete data from Last Order's mind through the manipulation of vectors of her bio-electricity.[5] Furthermore, Accelerator can do it even if he is unconscious, able to make an invisible "tube" to control blood flow in Yoshikawa Kikyou's artery and not allow a single drop to spill.[6] In fact, the combined brains of 10,000 level 3 Sisters are only able to make up less than half of Accelerator's calculating power, though it seems it is enough for Accelerator to use it even in combat.[7]

Accelerator uses this passive ability of "Redirection" or "Reflection" (反射,Hansha?, lit. "Reflection") to reverse any oncoming vector coming towards the field that protects his entire body, most likely his AIM Diffusion Field, which somehow covers even the clothes he wears and select objects he is holding. The redirection ability can be done subconsciously through some simple calculations as he was shown doing so as a child 5-6 years prior to the start of the story.[8] He just needs to calculate the minimum required forces like gravity, air pressure, light, oxygen, heat, sound wavelength, etc. and redirect everything else. Things such as light, sound, and gravity are calibrated to pass through this field for his convenience, though he can undo this if he chooses to.[9] For defensive use, Accelerator subconsciously establishes a filter that analyzes everything as harmful or not, and uses his reflect to push away anything that could harm him.[10] Examples of these would be high-velocity vectors that are reflected, such as bullets, which Accelerator obviously could not consciously react to, as the speed of a bullet is immensely high. He was also able to re-direct Misaka's Railgun.[11]

It is the default and the most basic use of Accelerator's power, allowing him to be protected from nearly any sort of attack, and he even boasts that with it he is able to even withstand a nuclear missile, shock-wave, heat, and radiation.[2] However, in his fight against Kamijo Touma after he causes a dust-explosion he mentions that it seems that he might not actually be able to survive it due to being deprived of oxygen in the center of vacuum created by the explosion.[12] Though he quickly counters that it becomes a none issue by simply having an oxygen tank on him about the size of a can of hairspray. It is this barrier that reflects anything harmful to him that gave him his infamous look. His albino appearance is because his body doesn't need to produce protection from the harmful UV rays as Accelerator's power does it for him which has caused his body to stop producing Melanin as it no longer needs to. Moreover, his androgynous appearance is due to his power, as their is lack of outside stimulus, there is an imbalance of hormones that gave him his looks.[13] It is said to even be able to reflect teleportation vectors in the 11th dimension, though a strange phenomenon would occur in the 3-dimensional world, so thus people could not teleport harmful objects into his body, as most teleporters would do in a battle. And with magic, information regarding magic attacks affecting his field is limited, though when Accelerator tried to redirect Vodyanoy's attack on his person it was not completely redirected but disintegrated into a rainbow of light.[14]

In the past, Accelerator may have not been able to control the redirection of vectors and may have been the cause of the incident where a group of children gets hurt due to his powers, leading to Academy City forces trying to take him down instead of malice in his part.[15]

The barrier for his redirection is not an absolute defense, as Kihara Amata has demonstrated. Since it only reverses the vectors that are coming towards him, any vector that comes towards his barrier and pulls away at the exact moment before hitting its field will go towards Accelerator.[16]

Furthermore, attacks that are built upon laws or vectors unknown to him can penetrate his defense, such as what Kakine Teitoku did with the light passing through his white wings[10] or the attacks that Aiwass made on him that cut him down.[17]

However, due to the nature of his power and Accelerator's massive calculating prowess, Accelerator can change the rules of his filter system.[10]

Finally, like all supernatural phenomena, the Imagine Breaker can bypass the field that protects Accelerator, though it is not known if he can negate the field.

Vector Control (ベクトル制御,Bekutoru Seigyo?, lit. "Vector Control") is the active effect of the Accelerator and requires active calculations in order to maintain it, as even a slight error can nullify the effect.[Excerpts 4] A seemingly recent discovery of Accelerator's due to his abuse of his Redirection, the effect allows Accelerator to manipulate vectors instead of redirecting them.[15] It is most likely this effect of being able control nearly everything in the world that Accelerator is described as "The One Who Wields the Power of God" (神にも等しい力の片鱗を振るう者,Kami nimo hitoshii chikara no henrin wo furuu mono?),[18] even more so now that he can analyze and understand different laws. Furthermore, it is this effect that allows Accelerator to use magic, though not without consequences.[1]

Kuroyoru Umidori's Bomber Lance is base off of this active effect.[4] The unique trait of this active effect is that it has many applications:

Accelerator's vector manipulation has a variety of uses, including crushing the earth around him.

Earthquake Generation: By altering the vector of force applied to the ground by his feet, he causes a little explosion made of earth and rocks to attack his opponents. At the beginning of the series this was his most common method of attack. He can also use this to propel himself forward, as seen in the Sisters Arc, or cause massive destruction to the ground and surrounding buildings due to shock-waves created by the impact, as seen during his scuffle with Awaki in the Tree Diagram Remnant Arc.

Tactile Telekinesis: By touching an object, he can use his ability to change the magnitude of vectors he comes in contact with, such as seen during his fight with Kamijou Touma in the Sisters Arc. This allows him to change the vectors of objects in such a way that he can turn them to projectiles. An example of the use of this ability is in his fight with Touma, when he lightly kicked a rock to make it shoot like a bullet, or when he stomped on train rails to push them out of their sockets, and lightly knocked on them to make those rails rain upon Touma. This ability also allows him to mimic superhuman strength, as he once used it to pick up and throw a concrete wall.

Aerokinesis: He can re-vector the surrounding winds and force them to congregate at a single point creating an extremely high velocity wind, but it had flaws like when the wind is moving in an abnormal direction or when his vector calculations are disturbed by sound as showed as with Kihara in the Volume 13.

Plasma Generation: He can even create plasma by further compressing the wind at high speeds in a single point.

Acceleration: By controlling the vectors around his body he can achieve inhuman speed.

Kinetic Energy Manipulation: Shown in Volume 13, he takes control of the planet's rotational vectors and transfers an enormous amount of that energy into one attack. This attack used up so much of the planets rotational energy that it slowed down the the earth's rotation by about 5 minutes.

Mind Hacking: In accord to him by redirecting the electrical signals of the human body he can take 'control' over them and rewrite the memories and personality of the people as showed with Last Order in the Vol.5. However this type of application is extremely difficult, as the precision of this process requires all his brainpower to a point when he doesn't have enough calculating ability for his redirection leaving him vulnerable. With Accelerator's calculation ability reduced to less than half, this application seems to be no longer usable.[19]

With his vector powers, Accelerator is easily able to catch up with a fleeing airborne Awaki.

Flight: By controlling the wind around him he creates about 4 high-powered tornadoes behind him to allow him to fly. Showed in Vol.8 and 15. He is also able to redirect the vectors of gravity upon him.

Sound Nullifying: Shown in Three Stories Arc, by controlling the vectors around his body and creating a second skin of vectors that nullifies sound.

Blood Control: By touching his opponent he can kill them by either reversing their blood flow or just exploding them. In Volume 19, where he was cut by the wings of Aiwass, he was able to survive because he used his ability and brought them through his destroyed veins. It seems like he can close his wound completely; only a few days later he travelled with Last Order in a train because he needed to find Index and his choker was on 'normal mode', which means he wasn't using his ability, in Volume 22 he used Index's 'Heal Song' and healed Last Order but couldn't prevent the backslash, his body destroyed itself, before that he was shot several times by Worst. After the WW3, where he gained a halo over his head and White Wings, it seemed like this wounds weren't a threat to him anymore, at least it wasn't mentioned that they would be a disadvantage to him.

Because the standard measurement is the worth of the ability to the ongoing research,[20] this ability is considered the most valuable ability in the entire Academy City. This ability is of great interest to the researchers, as evidenced by the large amount of research projects involving it.[21][4]

↑"It seemed the intellect that had directly developed the esper power known as Accelerator was quite something."―Toaru Majutsu no Index Volume 13 Chapter 10 Part 1

↑"He hit the switch off the electrode on his neck and the Level 5 powers that gave him his name activated."―Shinyaku Toaru Majutsu no Index Light Novel Volume 03 Chapter 2 Part 10

↑"The big bang at the start of the universe had yet to be proven to be a giant explosion. All that had been done was using giant ring-shaped particle accelerators to recreate and confirm the physical phenomena theorized to have happened after the explosion. Physicists used that to continually bring the original explosion as close as possible to reality in their minds as they filled in the details bit by bit."―Toaru Majutsu no Index Light Novel Volume 22 Chapter 11 Part 1